Penalized Joint Maximum Likelihood Estimation Applied to Two Parameter Logistic Item Response Models

Item response theory (IRT) models are a conventional tool for analyzing both small scale and large scale educational data sets, and they are also used for the development of high-stakes tests such as the Scholastic Aptitude Test (SAT) and the Graduate Record Exam (GRE). When estimating these models it is imperative that the data set includes many more examinees than items, which is a similar requirement in regression modeling where many more observations than variables are needed. If this requirement has not been met the analysis will yield meaningless results. Recently, penalized estimation methods have been developed to analyze data sets that may include more variables than observations. The main focus of this study was to apply LASSO and ridge regression penalization techniques to IRT models in order to better estimate model parameters. The results of our simulations showed that this new estimation procedure called penalized joint maximum likelihood estimation provided meaningful estimates when IRT data sets included more items than examinees when traditional Bayesian estimation and marginal maximum likelihood methods were not appropriate. However, when the IRT datasets contained more examinees than items Bayesian estimation clearly outperformed both penalized joint maximum likelihood estimation and marginal maximum likelihood.